Eichel, a 23-year-old center and the second overall pick in the 2015 NHL Draft, is on pace for a career season, leading Buffalo in goals (14) and assists (15).
The Panthers got goals from Brett Connolly and Noel Acciari. Connolly has five goals in his past five games and a team-high 11 for the season. Florida, which has lost two straight games, got 21 saves from rookie backup goalie Sam Montembeault.
It was Montembeault's first start since Nov. 10, and it was a success for him early on, as Florida dominated the first 16 minutes of the game, holding a 9-2 shots-on-goal advantage.
But then Eichel carried the puck into the zone, weaving around three Panthers defenders before threading the puck to Skinner, whose redirection on the doorstep beat Montembeault five-hole with 16:24 expired in the first.
Buffalo made it 2-0 less than two minutes later, as Girgensons took a drop pass from Brandon Montour and scored with a wrist shot from the left circle.
The Sabres extended their lead to 3-0 with 3:42 expired in the second, as Eichel got loose with a sweet move and then rang in a shot that went in off the left post.
Florida got on the board with 9:29 gone in the second when Acciari picked up a loose puck and beat Ullmark from point-blank range.
Buffalo got that goal back just a few minutes later, at the 14:41 mark. On a breakaway and with the Panthers giving chase, Olofsson beat Montembeault glove-side, ringing his shot in off the right post.
After Henri Jokiharju was penalized for tripping, Florida cashed in with Connolly's power-play goal from just above the left circle, making it 4-2 with 16:52 left in the third. After taking a pass from Aaron Ekblad, Connolly's blast went in off Ullmark's left arm.
Buffalo stretched its lead to 5-2 on Girgenson's second goal, this one with 6:35 left in the third.
--Field Level Media